{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:54:33Z","timestamp":1791554073899,"version":"4.3.4"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A local-volatility surface must reprice the vanilla grid under the finite-difference engine that values the book. Analytic Dupire surfaces frequently fail this round-trip test: on our SPX sample calibrated eSSVI surfaces misprice by 30 bp of implied volatility on a root-mean-square basis. The industry standard approach is to calibrate the surface numerically as in Andreasen and Huge (2011). This passes the round trip by construction if the surface fits the market but tends to produce a rough surface and unstable sensitivities. Numerical calibration can also be slow and with the typically large number of parameters may not converge to a global optimum. This paper develops an alternative approach that keeps the base surface and removes the residual with derivative-free bootstrap iterations forward over quoted maturities. The local-volatility slice for each time interval or tenor is scaled by a smoothed power of the ratio of market to model implied volatility, with the exponent updated by a secant regression on successive errors. No Jacobian of the pricing map is calculated; one pricing per sweep replaces the one-pricing-per-node of a derivative-based numerical optimization. This can be thought of as a smooth correction to the base surface, and the method is agnostic to the surface it corrects. We demonstrate it on two calibrated surfaces: the analytic Dupire surfaces derived from a Hendriks-Martini eSSVI fit, and the previous day's numerically calibrated surfaces re-interpolated onto today's strikes. Accuracy is benchmarked against a full Andreasen-Huge (AH) calibration. The data consist of daily SPX vol surfaces for the period from 22 June 2023 to 30 April 2026 (714 surfaces). All pricing is done by backward PDE in Numerix CrossAsset. With eSSVI as the base the pooled round-trip RMSE is 3.47 bp on volatility. Iterating from the previous day's surface (warm start) gives 3.88 bp against 3.34 bp for full AH calibrations. Uncorrected eSSVI and warm start return 30 bp and 67 bp respectively. At maturities out to two years, where most of the book's Vega sits, the correction is more accurate than the full calibration: 2.12 and 2.08 bp out to one year against 3.07 bp, and 2.55 and 2.64 bp out to two years against 3.02 bp. The corrected surface outperforms the benchmark on 68 percent of market days out to two years. Beyond two years the benchmark is more accurate, 5.05 bp against 7.11 bp. There the quotes are sparse, noisy and a year apart, a coarse spline cannot follow noisy strike structure, and in a bootstrap the long columns can only absorb what the already-fitted short slices leave them; the iteration reaches its projected fixed point and is limited by representation, not convergence. The stopping criteria are anchored to the benchmark's per-expiry empirical accuracy-its median slice error is 1.01 bp and its median maximum deviation 4.11 bp. Convergence takes a median of 14 sweeps per expiry from eSSVI and 5 from the warm start, 341 and 218 pricings per surface. The corrected surfaces are<\/jats:p>","DOI":"10.2139\/ssrn.7589198","type":"posted-content","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:37:46Z","timestamp":1791553066000},"source":"Crossref","is-referenced-by-count":0,"title":["A Derivative-Free Fixed-Point Method for Local Volatility Calibration"],"prefix":"10.2139","author":[{"given":"Vlad","family":"Pavlov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:37:46Z","timestamp":1791553066000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7589198"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7589198","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}